Preparation and testing of laterally graded multilayer with a double genetic algorithm and root mean square error...

Area of Science:

• Materials Science
• Optics
• Computational Physics

Background:

• Graded multilayers are essential for hard X-ray applications like reflection, collimation, and focusing.
• Current research focuses on improving performance in synchrotron radiation and high-performance X-ray sources.
• Reducing d-spacing errors in these multilayers is critical for achieving desired optical properties.

Purpose of the Study:

• To propose and validate a root mean square error optimization method (DGA-RMSE) for reducing d-spacing errors in graded multilayers.
• To achieve precise control over the d-spacing distribution and minimize thickness errors during fabrication.
• To enhance the accuracy of hard X-ray optical components.

Main Methods:

• Optical design to determine the theoretical d-spacing distribution (1.9–3.1 nm).
• Construction of a monotonic rate distribution line (RDL) as a polynomial function.
• Application of a double genetic algorithm (DGA-RMSE) to optimize the polynomial variables and minimize thickness error.
• Validation using grazing incidence X-ray reflectivity (GIXRR).

Main Results:

• The DGA-RMSE method converged to a root mean square error of 0.0065 nm.
• The optimized d-spacing distribution was achieved through convolution of a particle beam function and the polynomial RDL.
• Experimental measurements using GIXRR confirmed the theoretical calculations of thickness error.
• The method demonstrated precise selection of the RDL polynomial function.

Conclusions:

• The DGA-RMSE method effectively reduces d-spacing errors in graded multilayers.
• This approach improves precision in high-precision magnetron sputtering and mask technology.
• The findings contribute to the development of advanced hard X-ray optics for scientific research.